Mining Institute, Ural Branch, Russian Academy of Sciences, Perm, Russia:
A. A. Baryakh, Director, Doctor of Engineering Sciences, e-mail: bar@mi-perm.ru
N. A. Samodelkina, Principal Researcher, Candidate of Engineering Sciences
E. A. Telegina, Senior Researcher, Candidate of Engineering Sciences.

Uralkali, Bereznyaki, Russia:

E. K. Kotlyar, Technical Director

In terms of Upper Kama potash salt deposit, the authors perform mathematical modeling of stress–strains state of impermeable strata (IS) and analyze IS stability at varied rates of potash extraction. It is assumed that safe mining of IS is conditioned by total thickness of rock salt layers free from shearing and tensile cracks under deformation of undermined rock mass. The mathematical modeling of deformation and failure in IS involved elastoplasticity and plane strain conditions. Under consideration was a perfect elastoplastic medium where strains and stresses were related by the Hook law and ultimate stresses in the compression domain were defined by parabolic Mohr’s envelope. Numerical implementation of the mathematical modeling used the standard finite element method scheme based on Lagrange’s variational principle. The elastoplastic problem solution was obtained using the iteration procedure of the initial stress method. Localization of plastic strains was physically interpreted as failure of rocks in IS: in the compression domain—as a consequence of shearing cracks; in the tension domain—due to tensile cracks. The analysis of the state of the undermined rock mass involved increasing dynamic subsidence of ground surface. From the results of the analysis, extraction of up to 45% of reserves ensures liberal safety of IS right down to movement process completion. Up to 20–40% of the total thickness of rock salt strata get broken in this case. Increase in extraction to 50% results in discontinuity over almost entire IS due to formation of tensile cracks at the top of IS, which stimulates failure process. Given available abnormalities in the structure of IS in specific ground conditions, it is recommended to carry out mathematical modeling to obtain an amended estimate of extraction ratio that ensures safe undermining of IS.
The study was partly supported by the Russian Foundation for Basic Research, Grant No. 15-05-04988, and by the Ural Branch of the Russian Academy of Sciences, Fundamental Research Program.

1. Kudryashov A. I. Verkhnekamskoe mestorozhdenie soley (Verkhanekamskoe salt deposit). Moscow : Epsilon Plyus, 2013. 368 p.
2. Prugger F. F., Prugger A. F. Water problems in Saskatchewan mining — what can be learned from them? CIM Bulletin. 1991. Vol. 84, No. 945. pp. 58–66.
3. Rauche H. Sinkhole Formation over Flodded Potash Mines — Case Studies from the Motherland of the Potash Industry. Fall 2000 Meeting. San Antonio, Texas, USA, 2000. p. 161.
4. Whyatt J., Varley F. Catastrophic Failures of Underground Evaporite Mines. Proceedings of 27th International Conference on Ground Control in Mining. NIOSH. Spokane Research Laboratory, USA, 2008. pp. 17–23.

5. Krasnoshteyn A. E., Baryakh A. A., Sanfirov I. A. Gornotekhnicheskie avarii: zatoplenie Pervogo Bereznikovskogo kaliynogo rudnika (Mining-technical accidents: flood of the First Berezniki potash mine). Vestnik Permskogo nauchnogo tsentra = Bulletin of Perm Science Center. 2009. No. 2. pp. 4–9.
6. Wittke W. Rock Mechanics Based on an Anisotropic Jointed Rock Model (AJRM). Verlag : Wilhelm Ernst & Sohn, 2014. XIV. 875 p.
7. Popp, T., Minkley, W., Wiedemann, M., Salzer, K. Gas-pressure-induced integrity of salt formations. Geological Society Special Publication. 2015. Vol. 415, No. 1. pp. 107–122
8. Baryakh A. A., Samodelkina N. A. Ob odnom podkhode k reologicheskomu analizu geomekhanicheskikh protsessov (About an approach to rheological analysis of geomechanical processes). Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh = Journal of Mining Science. 2005. No. 4. pp. 32–41.
9. Kuznetsov G. N. Mekhanicheskie svoystva gornykh porod (Mechanical properties of rocks). Moscow : Ugletekhizdat, 1947. 180 p.
10. Seryakov V. M. Ob odnom sposobe ucheta reologicheskikh svoystv gornykh porod pri raschete napryazhenno-deformirovannogo sostoyaniya massiva v zone podrabotki (The inclusion of rheological properties of rocks to calculation of stress-strain state of an undermined rock mass). Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh = Journal of Mining Science. 2010. No. 6. pp. 18–24.
11. Zienkiewicz O. C. The finite element method in engineering science. London : McGraw-Hill, 1975. 578 p.
12. Malinin N. N. Prikladnaya teoriya plastichnosti i polzuchesti (Applied theory of plasticity and creep). Moscow : Mashinostroenie, 1975. 400 p.
13. Turchaninov I. A., Iofis M. A., Kasparyan E. V. Osnovy mekhaniki gornykh porod (Basis of rock mechanics). Leningrad : Nedra, 1989. 488 p.
14. Baryakh A. A. Samodelkina N. A. Razrushenie vodoupornykh tolshch pri krup no masshtabnykh gornykh rabotakh. Chast 2 (Water-tight stratum rupture under large-scale mining. part II). Fiziko-tekhnicheskie problemy razrabotki poleznykh iskopaemykh = Journal of Mining Science. 2012. No. 6. pp. 12–20.